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A129862
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Triangle read by rows: row n gives coefficients of characteristic polynomial of the Cartan matrix for the root system D_n.
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1
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2, 2, -1, 4, -4, 1, 4, -10, 6, -1, 4, -20, 21, -8, 1, 4, -34, 56, -36, 10, -1, 4, -52, 125, -120, 55, -12, 1, 4, -74, 246, -329, 220, -78, 14, -1, 4, -100, 441, -784, 714, -364, 105, -16, 1, 4, -130, 736, -1680, 1992, -1364, 560, -136, 18, -1, 4, -164, 1161, -3312, 4950, -4356, 2379, -816, 171, -20, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Absolute values of the rows sums are 2, 3, 9, 21, 54, 141, 369, 966, 2529, 6621, 17334
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REFERENCES
| R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 60
Sigurdur Helgasson,Differential Geometry, Lie Groups and Symmetric Spaces,Graduate Studies in Mathematics, volume 34. A. M. S. :ISBN 0-8218-2848-7, 1978,p. 464
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FORMULA
| M(d)=If[ n == m, 2, If[(m == d &&n == d - 2) || (n == d && m == d - 2), -1, If[(n == m - 1 || n == m + 1) && n <= d - 1 && m <= d - 1, -1, 0]]]; At row level d : t(n,m)=CoefficientList[CharacteristicPloynomial[M(d),x],x]
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MATHEMATICA
| T[n_, m_, d_] := If[ n == m, 2, If[(m == d && n == d - 2) || ( n == d && m == d - 2), -1, If[(n == m - 1 || n == m + 1) && n <= d - 1 && m <= d - 1, -1, 0]]]; M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}];
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CROSSREFS
| Cf. A127677, A005248.
Sequence in context: A129903 A023616 A099491 * A138189 A110090 A196831
Adjacent sequences: A129859 A129860 A129861 * A129863 A129864 A129865
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KEYWORD
| tabf,uned,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 23 2007
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